Quasi-static deformation due to a dislocation source in a Maxwellian viscoelastic earth model.

Abstract

In this paper, we treat quasi-static deformation field due to a dislocation source in a composite medium which consists of elastic layers overlying a strat-ified viscoelastic half-space. The rheologies of the viscoelastic layers are as-sumed to be elastic dilatational and Maxwell deviatoric. Integral representa-tions of the surface displacements are derived from those in the associated elastic problem by applying the correspondence principle of linear viscoelastici-ty. The effect of gravity is taken into account by modifying the boundary con-ditions with respect to normal stress. Features of the viscoelastic displacements are investigated for a three-layered structure model composed of an elastic surface layer, an intervening low viscosity layer, and a viscoelastic substratum with relatively high viscosity. A dislocation source is supposed to be located in the elastic surface layer. The effect of the stress relaxation in the substratum is examined for both a point source and a dimensional fault. Difference in the viscosity of the substratum affects the amount and extent of the viscoelastic deformation. In a model with a low viscous substratum, the amount of displacement is large and the deformation spreads in a broad area. The effect of gravity is investigated assuming a pure dip-slip fault. The viscoelastic deformation for the gravitating case is restrained in amount and extent as compared with the non-gravitating case. Such an effect of gravity becomes notable with time. In the gravitating case, the stress relaxation progresses fast, and the apparent relaxation time of deformation is much shorter than that for the non-gravitating case.